On statistical and deterministic quantum teleportation

Abstract

We generalize quantum teleportation to, what we call, statistical teleportation utilizing previous results on distant preparation, and on the basic ingredient entities of an entangled composite-system state vector. Our main result is 'the central theorem', establishing a simple necessary and sufficient condition for the crucial entity: the event that the sender of a pure quantum state has to measure in the first step of the two-step (and two-laboratory) teleportation procedure. We derive numerous consequences especially for deterministic teleportation (a special case of statistical teleportation), which is a direct generalization of the known quantum teleportation. Detailed further generalization to proper and improper mixtures is investigated. Finally, it is shown that extension to teleportation with nonlinear distant preparation is not possible unless the idea of teleportation is essentially changed.